Feb 2025 Angles in Polygons and Parallel Lines PDF

Medium Questions 1 ABC and DEF are parallel lines. BEG is a straight line. Angle GEF = 47°. Work out the size of the angle marked x. Give reasons for your answer. (3 marks)...

Medium Questions 1 ABC and DEF are parallel lines. BEG is a straight line. Angle GEF = 47°. Work out the size of the angle marked x. Give reasons for your answer. (3 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 2 2 ABC , PQR and AQD are straight lines. ABC is parallel to PQR. Angle BAQ = 35° Angle BQA = 90° Work out the size of the angle marked x. Give reasons for each stage of your working. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 3 3 PRS and TWY are parallel straight lines. QRWZ is a straight line. Work out the value of x. Give reasons for your answer. (3 marks) 4 ABC , DEF and PQRS are parallel lines. BEQ is a straight line. © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 4  Angle ABE = 60°. Angle QER = 80°. Work out the size of the angle marked x. Give reasons for each stage of your working. (4 marks) 5 The diagram shows a regular octagon and a regular hexagon. Find the size of the angle marked x. You must show all your working. (3 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 5 6 ABCDE and PQRST are regular pentagons. SR is parallel to DC. AP = BQ = CR = DS = ET Work out the size of angle SRC. You must show all your working. (3 marks) 7 RS and ST are 2 sides of a regular 12-sided polygon. RT is a diagonal of the polygon. © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 6  Work out the size of angle STR. You must show your working. (3 marks) 8 CDEF is a straight line. AB is parallel to CF. DE = AE. Work out the size of the angle marked x. You must give reasons for your answer. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 7 9 ABCDE is a pentagon. Angle BCD = 2 × angle ABC. Work out the size of angle BCD. You must show all your working. (5 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 8 10 Here is a 10-sided polygon. Work out the value of x. x =................................................. (4 marks) 11 Each interior angle of a regular polygon is 162° Work out the number of sides the polygon has. (3 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 9 12 The diagram shows a triangle. Work out the value of x. x =.................. (4 marks) 13 The diagram shows a parallelogram ABCD and an isosceles triangle DEF in which DE = DF © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 10  CDF and ADE are straight lines. Angle BCD = 58° Work out the size of angle DEF. Give a reason for each stage of your working. (5 marks) 14 What is the size of an exterior angle of a regular decagon? Circle your answer. 18° 36° 144° 162° (1 mark) 15 The exterior angle of a regular polygon is 45° Circle the name of the regular polygon. pentagon hexagon octagon decagon © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 11  (1 mark) 16 Part of a regular polygon with 15 sides is shown. Work out the size of an interior angle.....................................................degrees (2 marks) 17 The sum of the angles in any quadrilateral is 360° For example, in a rectangle 4 × 90° = 360° Zak writes, 5 × 90° = 450° so the sum of the angles in any pentagon must be 450° Is he correct? Tick a box. □ Yes □ No Show working to support your answer. (2 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 12 18 Here is a sketch of a quadrilateral. All lengths are in centimetres. Tick one box for each statement. True May be true Not true The quadrilateral is a rectangle The quadrilateral is a parallelogram The quadrilateral is a rhombus The quadrilateral is a kite (3 marks) 19 Tick all the statements that are true for any rhombus. © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 13 □ The diagonals are lines of symmetry □ The diagonals bisect each other □ The diagonals are perpendicular □ The diagonals are equal in length (1 mark) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 14 20 (a) Work out the size of the exterior angle of a regular 12-sided polygon. (2 marks) (b) Use your answer to part (a) to write down the size of the interior angle of a regular 12- sided polygon. (1 mark) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 15 21 (a) The diagram shows triangle ABC. CD is parallel to AB. A, C and E lie in a straight line. Angles of size a °, b ° and c ° are shown. Insert a °, b °° or c ° to make this statement true. Give a reason for your answer. Angle DCE =......... because.................................................................................................... (2 marks) (b) Use the diagram and the answer to part (a) to show that the angles of a triangle add up to 180°. Give a reason for each statement you make. (3 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 16 Hard Questions 1 ABCD is a parallelogram. Angle ADB = 38°. Angle BEC = 41°. Angle DAB = 120 °. Calculate the size of angle x. You must give reasons for your answer. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 17 2 ABC is parallel to EFGH. GB = GF Angle ABF = 65° Work out the size of the angle marked x. Give reasons for your answer. (4 marks) 3 ABCD and EFG are parallel lines. BC = CF Angle BFE = 70° © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 18  Work out the size of the angle marked x. Give reasons for each stage of your working. (4 marks) 4 ABC and DE are parallel lines. AEG and BEF are straight lines. Angle AED = 54° Angle FEG = 70° Work out the size of the angle marked x. Give a reason for each stage of your working. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 19 5 ABC and EDC are straight lines. AE and BD are parallel. Angle ABD = 125 ° Angle BCD = 30° Work out the size of the angle marked x. Give reasons for your answer. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 20 6 ABCD is a parallelogram. EDC is a straight line. F is the point on AD so that BFE is a straight line. Angle EFD = 35° Angle DCB = 75° Show that angle ABF = 70° Give a reason for each stage of your working. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 21 7 AE , DBG and CF are parallel. DA = DB = DC. Angle EAB = angle BCF = 38° Work out the size of the angle marked x. You must show your working. (3 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 22 8 The diagram shows a pattern using four identical rhombuses. Work out the size of the angle marked a. You must show your working. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 23 9 ABCDEFGH is a regular octagon. BCKFGJ is a hexagon. JK is a line of symmetry of the hexagon. Angle BJG = angle CKF = 140° Work out the size of angle KFE. You must show all your working. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 24 10 The diagram shows part of a pattern made from tiles. The pattern is made from two types of tiles, tile A and tile B. Both tile A and tile B are regular polygons. Work out the number of sides tile A has. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 25 11 ABCDE is a regular pentagon. ACFG is a square. Work out the size of angle DCF. You must show all your working. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 26 12 ABCDEFGH is a regular octagon. KLQFP and MNREQ are two identical regular pentagons. Work out the size of the angle marked x. You must show all your working. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 27 13 In the diagram, AB , BC and CD are three sides of a regular polygon P. Show that polygon P is a hexagon. You must show your working. (4 marks) 14 Here is a parallelogram. Work out the value of x and the value of y. © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 28  (5 marks) 15 The diagram shows a square and 4 regular pentagons. Work out the size of the angle marked x. (3 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 29 16 AGC and DEF are parallel lines. ADB and GE are parallel lines. BEC is a straight line. Angle DBE = 95° Angle CGE = 55° Work out the size of the angle marked x. Give reasons for each stage of your working. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 30 17 ABCDE is a regular pentagon. BCF and EDF are straight lines. Work out the size of angle CFD. You must show how you got your answer. (3 marks) 18 Here is a quadrilateral. a = 90° and a : b = 5 : 3 © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 31 x:y = 1:3 Show that b = x (3 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 32 19 (a) An interior angle of an isosceles triangle is p° and an exterior angle is q °. It is given that q = 5p. Write the ratio p : q in its simplest form. (2 marks) (b) Work out the two different possible sets of angles for the isosceles triangle. Triangle 1:............°,.............°,.............° Triangle 2:............°,.............°,.............° (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 33 Very Hard Questions 1 The diagram shows a regular pentagon. AB and CD are two of the lines of symmetry of the pentagon. Work out the size of the angle marked x. You must show all your working. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 34 2 Here is a pentagon ABCDE. AB = BC = BD ABDE is a kite. Angle AED = 40° Angle EDB = 130 ° Angle BDC = 72° Work out the size of angle ACB. (3 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 35 3 ABCDEFGHI is a regular 9-sided polygon. The vertices B and E are joined with a straight line. Work out the size of angle BEF. You must show how you get your answer. (4 marks) 4 The diagram shows a hexagon. © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 36 The hexagon has one line of symmetry. FA = BC EF = CD Angle ABC = 117 ° Angle BCD = 2 × angle CDE. Work out the size of angle AFE. You must show all your working. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 37 5 PQRST is a regular pentagon. R , U and T are points on a circle, centre O. QR and PT are tangents to the circle. RSU is a straight line. Prove that ST = UT. (5 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 38 6 The diagram shows a regular 10-sided polygon, ABCDEFGHIJ Show that x = y. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 39 7 The diagram shows a regular octagon ABCDEFGH and a regular pentagon ABIJK Work out the size of the angle x. (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 40 8 AB , BC , CD and DE are four of the sides of a regular decagon. Work out the size of angle w...............................degrees (3 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 41 9 (a) AB , CD and EF are straight lines. Ava assumes that AB and CD are parallel. What answer should she get for the size of angle y ?...............................degrees (4 marks) (b) In fact, AB and CD are not parallel angle w is 60° What effect does this have on the size of angle y ? Tick a box. © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 42  □ y is bigger □ y is the same □ y is smaller Show working to support your answer. (3 marks) 10 AB , CD and YZ are straight lines. All angles are in degrees. Show that AB is parallel to CD. © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 43  (4 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 44 11 (a) Imran joins two tiles together as shown below. One tile is a regular hexagon and the other tile is a regular pentagon. Show that angle a is 132°. (3 marks) (b) Imran thinks that another tile in the shape of a regular polygon will fit exactly into angle a. Is Imran correct? Show your reasoning. (3 marks) 12 Angle BAE is part of a regular 18-sided polygon. Angle CAD is part of a regular 10-sided polygon. © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 45 The dashed line through A is a line of symmetry of both polygons. Work out angle BAC. (5 marks) © 2025 Save My Exams, Ltd. Get more and ace your exams at savemyexams.com 46